I have a neighbor who works from home and drives in and out of the subdivision more. I am guessing but I suppose he traverses our subdivision road in and out perhaps 6 times a day, or 24/600 minutes, or 1/25th of the day, or 0.04 of the day.

Here's my problem. I encounter my neighbor on that road

**a LOT**, at least 15% of the time, or 1/6 trips. That is weird and not statistically probable.

So, what is the probability that we will both be driving down that subdivision road simultaneously, and pass or see each other on the road?

I thought I knew. To compute the probability of two events (both driving the road) occurring simultaneously, textbooks say you simply multiply the two individual probabilities, but that can't be right. If I did so, then 0.00666 x 0.04 = 0.0002664, which is a very small and very incorrect number. To prove it, imagine that my neighbor was always driving on our subdivision road, back and forth, for 10 hours a day. His probability of being there would be 600/600 minutes or 1.0. If I multiplied his probability and mine (0.00666), I would get 1.0 x 0.00666 = 0.00666, or 0.6% probability that we would see each other on the road. That is clearly wrong. If he was always on the road, I would see him 100% of the time I drove down the road, not 0.66%. So, clearly in this case, computing the probability of encountering my neighbor on my subdivision road at the same time I was on it by simply multiplying both independent probabilities, is NOT the correct solution.

So what is the correct answer?